单元质量评估(三)
2013麒麟高中高二生物精品练习：单元质量评估(三) (必修2)
单元质量评估(三)第4章(90分钟100分)一、选择题(共25小题，每小题2分，共50分)1.某同学在无菌培养基上接种酵母菌后，不久就出现了酵母菌菌落，该菌落属于( )A.种群B.群落C.细菌斑D.生态系统2.你认为下列调查动物种群密度的方法中，正确的是( )A.可采用样方法调查草地中跳蝻的种群密度B.可采用样方法调查草地中野兔的种群密度C.用标志重捕法调查土壤中小动物的种群密度D.用标志重捕法调查土壤中昆虫卵的种群密度3.(2011·临沂高二检测)下列有关种群和群落的研究和分析中，正确的是( )A.田鼠在被捉过一次后更难捕捉，统计得到的种群密度比实际数值要低B.对培养液中酵母菌进行计数采用的是抽样检测法C.对小动物的种群密度进行调查时，不能采用标志重捕法，一定要采用样方法D.某同学决定以校园内的池塘为对象进行物种丰富度调查，应在同一水层取样4.(2011·北京高考)在生态学研究中，下列方法与研究目的不相符的是( )A.给海龟安装示踪器调查其洄游路线B.给大雁佩戴标志环调查其迁徙路线C.用样方法研究固着在岩礁上的贝类的种群关系D.用标志重捕法调查达乌尔黄鼠的丰富度5.下列各项中，不属于对种群数量特征描述的是( )A.我国的人口将逐渐步入老龄化阶段B.第六次人口普查中，成都的人口出生率为6.77%C.橡树种子散布能力差，常在母株周围形成集群D.由于薇甘菊的入侵，松树种群的死亡率比较高6.据预测，我国人口数量在2050年将达到最高值，作出这一预测的依据是( )A.各年龄期人口的比例B.现有人口数量密度C.出生率、死亡率和迁入率、迁出率D.人口性别比例7.如图表示的是四个不同种群中不同年龄期的个体所占的比例，其中种群密度可能越来越小的是( )8.长期生活在某环境中的种群，其数量变化最可能的是( )A.呈“J”型或“S”型曲线增长B.增长、波动C.波动、稳定D.增长、下降9.种群是生态研究的一个重要单位，有关种群的叙述正确的是( )A.种群是指一个生态系统中同种生物所有成熟个体的总和B.一个呈“S”型增长的种群中，种群增长率在各个阶段是不同的C.种群中各年龄期的个体数目比例适中，这样的种群正处于发展阶段D.合理密植农作物时，其数量可以大于K值10.下列几组图中，能正确表示生存斗争、种间斗争、种内斗争和竞争关系的是( )11.如图表示处于平衡状态的某生物种群因某些外界环境变化导致种群中生物个体数量改变时的四种情形，下列对产生这些变化的原因分析，正确的是( )(1)若图①所示为草原生态系统中的某种群，则a点后变化的可能原因是过度放牧(2)若图②所示为某发酵罐中的菌种数量，则b点后变化的原因可能是增加营养供应(3)图③中c点后发生的变化表明生态系统遭到了破坏(4)图④曲线可用于指导海洋捕捞A.只有一种说法正确B.只有两种说法正确C.只有三种说法正确D.四种说法都正确12.下列对探究培养液中酵母菌种群数量动态变化实验的叙述，错误的是( )A.从试管中吸出培养液之前应振荡试管，有利于正确计数B.先将培养液滴在计数板上，轻盖盖玻片防止气泡产生C.当一个小方格中酵母菌数量过多时，应将培养液按比例稀释处理D.压在方格边上的酵母菌，只计数相邻两边及其顶角的个体数13.有一种紫腹巨蚊，当它处于幼虫状态时，专以毒蚊幼虫为食，当它发育成成虫后，又以吸食竹类植物的叶汁花浆为生。
选择题 政治 人教版 必修一 第三单元 收入与分配
单元质量评估(三)1．按劳分配是社会主义公有制经济中个人消费品分配的基本原则。
实行按劳分配的直接原因是() A．生产资料公有制B．生产力的发展水平C．多种分配方式并存D．社会主义条件下人们劳动的性质和特点2．居民购买国债所得属于按资本要素分配取得的收入，下列对这一分配方式认识正确的是() A．它是提高居民收入的主要途径B．它是个人消费品分配的主要方式C．它是与市场经济相适应的收入分配方式D．它是由生产资料公有制决定的分配方式3．刘月的爸妈承包集体土地种粮年收入1.5万元，收购、销售蔬菜年收入4万元，房屋出租年收入5千元。
其中属于按劳分配的收入为()A．6万元B．5.5万元C．4万元D．1.5万元4．广东某国家控股的药业有限公司与三位博士合办一家新的有限责任公司，原公司注册300万元拥有70%的股份，三位年轻博士以“无形资产”——知识拥有30%的股份，这种合办既实现了科技成果的产业化，又实现了个人技术与国有资产的结合。
这三位博士取得的收入属于()A．按劳分配所得B．按劳动要素分配所得C．按生产要素分配所得D．按劳分配与按生产要素分配所得5．从2012年1月1日起，南京市事业单位统一实施绩效工资，并同步推进和实施事业单位养老保险制度。
绩效工资是指根据工作成绩和劳动效率确定的工资。
事业单位实施绩效工资()①与社会主义公有制经济中个人消费品分配的基本原则相吻合②有利于调动事业单位劳动者的积极性，提高服务质量③有利于增加事业单位劳动者的工资收入④实现了按劳分配和按生产要素分配的统一A．①②B．②③C．②④D．③④6．下列对我国分配方式理解不正确的是()①劳动收入属于按劳分配，非劳动收入属于按生产要素分配②按劳分配体现效率优先，其他分配方式体现兼顾公平③按劳分配为主体、多种分配方式并存④按劳分配存在于公有制经济中，其他分配方式存在于非公有制经济中A．①②③④B．①②③C．②③④D．①②④7．“十二五”规划纲要提出，要“努力实现居民收入增长和经济发展同步、劳动报酬增长和劳动生产率提高同步”。
化学反应原理：单元质量评估(三)
单元质量评估(三)第三章(90分钟 100分)一、选择题(本题包括16小题，每小题3分，共48分)1.(双选)硫酸锶(SrSO4)在水中的沉淀溶解平衡曲线如下。
下列说法正确的是( )A.温度一定时，K sp(SrSO4)随c(SO42-)的增大而减小B.三个不同温度中，313 K时K sp(SrSO4)最大C.283 K时，图中a点对应的溶液是不饱和溶液D.283 K下的SrSO4饱和溶液升温到363 K后变为不饱和溶液2.喷墨打印机墨汁的pH为7.5～9.0。
当墨汁喷在纸上时，生成不溶于水的固体。
由此可知( )①墨汁偏碱性②墨汁偏酸性③纸张偏酸性④纸张偏碱性A.①③B.②④C.①④D.②③3.在25 ℃时，用蒸馏水稀释1 mol·L-1氨水至0.01 mol·L-1，随溶液的稀释，下列各项中始终保持增大趋势的是( )A.32c(OH ) c(NH H O)- B.c(H )c(OH )+- C.324c(NH H O)c(NH )+D.c(OH -)4.有①、②、③三瓶体积相等，浓度都是1 mol ·L -1的HCl 溶液，将①加热蒸发至体积减小一半；在②中加入少量CH 3COONa 固体(加入后溶液仍呈强酸性)；③不作改变。
然后以酚酞作指示剂，用NaOH 溶液滴定上述三种溶液，所消耗NaOH 溶液的体积是( )A.①=③＞②B.③＞②＞①C.③=②＞①D.①=②=③5.(2012·烟台高二检测)相同体积的pH=3的强酸溶液和弱酸溶液分别跟足量的镁完全反应，下列说法中正确的是( ) A.弱酸溶液产生较多的氢气 B.强酸溶液产生较多的氢气 C.两者产生等量的氢气 D.无法比较两者产生氢气的量6.已知次氯酸是比碳酸还弱的酸，氯水中存在平衡Cl 2+H 2OHCl+HClO ，HClOH ++ClO -。
达平衡后，要使HClO 浓度增大，可加入( )A.H 2SB.Na 2CO 3C.盐酸D.NaOH7.(双选)(2012·徐州高二检测)下列溶液中有关离子浓度的说法可能正确的是( )A.NH4Cl溶液：c(Cl-)>c(NH4+)>c(OH-)>c(H+)B.Na2CO3溶液中：c(Na+)+c(H+)=c(HCO3-)+c(OH-)+c(CO32-)C.显酸性的CH3COOH与CH3COONa的混合溶液：c(CH3COO-)>c(Na+)>c(H+)>c(OH-)D.在NaHCO3溶液中：c(Na+)=c(HCO3-)+c(CO32-)+c(H2CO3)8.(2012·苏州高二检测)二元酸H2A在水中发生电离：H2A====H++HA-和HA-H++A2-，则下列几种物质的水溶液中关系式不正确的是( )A.NaHA：c(Na+)>c(HA-)>c(OH-)>c(H+)B.NaHA：c(Na+)=c(A2-)+c(HA-)C.Na2A：c(Na+)>c(A2-)>c(OH-)>c(H+)D.H2A：c(H+)=c(HA-)+2c(A2-)+c(OH-)9.在蒸发皿中加热蒸干并灼烧(低于400 ℃)下列的溶液，可以得到该物质的固体是( )A.氯化镁溶液B.硫酸亚铁溶液C.碳酸氢钠溶液D.硫酸铝溶液10.常温下，一定浓度的某溶液，由水电离产生的c(OH-)=10-4mol·L-1，则该溶液中的溶质可能是( )A.Al2(SO4)3B.CH3COONaC.NaOHD.KHSO411.已知当NH4Cl溶液的浓度小于0.1 mol·L-1时，其pH＞5.1。
2013麒麟高中高一地理精品课件：单元质量评估(三)
【解析】22选C，23选A。第22题，由图中此地区的海拔较低
及地势起伏较为和缓可以判断此地区的地形类型为丘陵。第
23题，由图中等高线的状况可以看出公路穿越的中间部位为 鞍部，海拔相对较低，等高线较为稀疏，坡度小，易于施工 和车辆的通行。
（2011·厦门高一检测）某市某中学开展地理观测活动，
图中各点是a、b、c、d四个小组以村庄M为基点的实测相对
从赤道到两极
从沿海到内陆降水量逐渐减少
（3）西北季风越过日本海带来大量水汽，在C地受地形抬升；
冬季因气温较低形成大量降雪。
27.（2010·昆明高一检测）读下面两幅图，回答下列问题。
（12分）
（1）非洲自然带从热带雨林带-热带草原带-热带荒漠带的
变化，明显地反映出陆地环境_______的地域分异规律，这 一规律的形成是以_______的变化为基础的。 （2）A处热带荒漠带向北延伸较远，主要是因为受_______ 影响，属于自然带分布的_______（地带性或非地带性）现 象。 （3）下图中自然带的更替现象，叫做＿＿＿，造成这种分 异的主要原因是＿＿＿。
【解析】17选A，18选D，19选B。第17题，图中四个居民点 均沿河分布，靠近水源，其中②③④三地位于河谷平原地区，
地势较低，易受水患影响。而①地位于地势稍高的鞍部地带，
受水患影响小。第18题，根据指向标可以判断①居民点应位 于②居民点的西南方向；M点与⑤地之间有山脊阻挡视线；
根据图中指向标的指示，河流①～②段从西南流向东北；由
洋面封冻，会阻断洋流的热输送，二者都会导致气候变冷， 气候变冷与洋面封冻面积扩大又会相互促进。光合作用减弱，
使二氧化碳吸收减少，导致大气二氧化碳比例上升，引起温
室效应，进而引起全球变暖。第13题，当前最有可能出现的 是由于大气中二氧化碳增多引发全球变暖，海平面上升，进 而导致世界各国经济结构的变化。但B项和D项分别是由酸雨 和臭氧层破坏引起的。
单元质量评估(三)(北师大版选修2-1)
单元质量评估(三)第三章 圆锥曲线与方程 (120分钟 150分)一、选择题(本大题共12小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的)1.(2011·湖南高考)设双曲线222x y 1a 9-=(a>0)的渐近线方程为3x ±2y=0,则a 的值为( )(A)4 (B)3 (C)2 (D)12.若椭圆的对称轴为坐标轴，长轴长与短轴长的和为18，焦距为6，则椭圆的方程为( )(A)22x y 1916+=(B)22x y 12516+=(C)2222x y x y 1125161625+=+=或(D)以上都不对3.(2011·许昌高二检测)已知抛物线y 2=2px(p ＞0)，过其焦点且斜率为1的直线交抛物线于A 、B 两点，若线段AB 的中点的纵坐标为2，则该抛物线的准线方程为( )(A)x=1 (B)x=-1 (C)x=2 (D)x=-24.中心在原点，焦点在x 轴上的双曲线的一条渐近线经过点(4，-2)，则它的离心率为( )225.(2011·广东高考)设圆C 与圆x 2+(y-3)2=1外切，与直线y=0相切，则C 的圆心轨迹为( )(A)抛物线 (B)双曲线 (C)椭圆 (D)圆6.连接抛物线x 2=4y 的焦点F 与点M(1，0)所得的线段与抛物线交于点A ，设点O 为坐标原点，则三角形OAM 的面积为( )32327.椭圆2222x y 1a b+=(a ＞b ＞0)的左焦点为F ，A(-a ，0)和B(0，b)是两个顶点，若F到直线AB 的距离为7，则椭圆的离心率为( )12 (D)458.(2011·张家界高二检测)椭圆2222x y 1a b += (a ＞b ＞0)则双曲线2222x y 1a b -=的离心率为( )(A)54329.以正方形ABCD 的相对顶点A 、C 为焦点的椭圆，恰好过正方形四边的中点，则该椭圆的离心率为( )10.设抛物线y 2=8x 的焦点为F ，准线为l ，P 是抛物线上的一点，PA ⊥l ，A 为垂足，如果直线AF 的斜率为|PF|=( )(A)11.(2011·新课标全国高考)已知直线l 过抛物线C 的焦点，且与C 的对称轴垂直，l 与C 交于A ，B 两点，|AB|=12，P 为C 的准线上的一点，则△ABP 的面积为( )(A)18 (B)24 (C)36 (D)4812.(2011·兰州高二检测)连接双曲线2222x y 1a b -=(a ＞0，b ＞0)与2222y x 1b a-=(a ＞0，b ＞0)的四个顶点的四边形面积为S 1，连接其四个焦点的四边形面积为S 2，则12S S 的最大值是( )(A)2 (B)4 (C)14(D)12二、填空题(本大题共4小题，每小题4分，共16分，请把正确的答案填在题中的横线上)13.(2011·大庆高二检测)已知抛物线y 2=4x 焦点F 恰好是双曲线2222x y 1a b-=的右焦点，且双曲线一条渐近线过点(23a 2，b)，则该双曲线的渐近线方程为 .14.以双曲线22y x 13-=的右焦点为圆心，离心率为半径的圆的方程是 .15.在一椭圆中以焦点F 1，F 2为直径的圆，恰好过短轴的两顶点，则此椭圆的离心率e ＝ .16.(2011·新课标全国高考)在平面直角坐标系xOy 中，椭圆C 的中心为原点，焦点F 1，F 2在x 过F 1的直线l 交C 于A ，B 两点，且△ABF 2的周长为16，那么C 的方程为 .三、解答题(本大题共6小题，共74分，解答时应写出必要的文字说明、证明过程或演算步骤)17.(12分)双曲线的离心率等于2，且与椭圆22x y 1259+=有相同的焦点，求此双曲线的标准方程.18.(12分)某抛物线形拱桥跨度是20米，拱高4米，在建桥时每隔4米需用一支柱支撑，求其中最长的支柱的长.19.(12分)在直角坐标系中，以M(-1，0)为圆心的圆与直线相切. (1)求圆M 的方程；(2)已知A(-2，0)、B(2，0)，圆内动点P 满足|PA|·|PB|=|PO|2，求PA PB的取值范围.20.(12分)过点(0，4)，斜率为-1的直线与抛物线y 2=2px(p ＞0)交于两点A 、B ，如果弦|AB|的长度为. (1)求p 的值；(2)求证：OA ⊥OB(O 为原点).21.(12分)(2011·孝感高二检测)已知椭圆22x y 14+=的左、右顶点分别为A 、B ，曲线E 是以椭圆的中心为顶点，B 为焦点的抛物线. (1)求曲线E 的方程；(2)直线l 与曲线E 交于不同的两点M 、N.当AM AN≥17时，求直线l 的倾斜角θ的取值范围.22.(14分)(2011·北京高考)已知椭圆G ：2222x y 1a b +=(a ＞b ＞0)右焦点为(0)，斜率为1的直线l 与椭圆G 交于A ，B 两点，以AB 为底边作等腰三角形，顶点为P(-3,2). (1)求椭圆G 的方程； (2)求△PAB 的面积.答案解析1.【解析】选C.由222x y 1a 9-=可得到双曲线的渐近线方程为y=〒3a x,又已知双曲线的渐近线方程为3x 〒2y=0,根据直线重合的条件可得到a=2. 2. 【解析】选C.由题意2a 2b 182c 6+=⎧⎨=⎩，又a 2=b 2+c 2. 解得：a=5,b=4,∴椭圆方程为2222x y x y 11.25161625+=+=或3.【解析】选B.设A(x 1，y 1)，B(x 2，y 2)，则由211222y 2px y 2px ⎧=⎪⎨=⎪⎩，得:(y 1-y 2)(y 1+y 2)=2p(x 1-x 2)， 即121212y y 2px x y y -=-+，∴1=2p4，∴p=2， ∴抛物线的准线为x=-1.4.【解析】选D.易知双曲线的渐近线方程为y=-12x ， ∴=5.【解析】选A.由题意，C 的圆心到点(0，3)与直线y=-1的距离相等，由抛物线的定义知C 的圆心轨迹为抛物线，故选A.6.【解析】选B.由题意得F 的坐标为(0，1).又点M(1，0)，故线段MF 所在直线的方程为x+y=1(0≤x ≤1). 解2x y 1(0x 1)x 4y+=≤≤⎧⎨=⎩， 得交点A 的坐标为，∴S △OAM =12〓1〓327.独具【解题提示】由点F 到直线AB出关系式，消去b 后构造关于c a的方程，解方程求c a，即离心率e. 【解析】选C.直线AB 的方程为bx-ay+ab=0， F(-c ，0)，∴7， ∴5a 2-14ac+8c 2=0， ∴8e 2-14e+5=0，解得:e=12.8.【解析】选B.由题意椭圆中=∴22b 1a 4=， ∴双曲线中=9.【解析】选D.如图所示，令|AC|=2c ， 则，|EC|=2c ，2a =， ∴e=c a ==10.独具【解题提示】解答本题可借助直线AF 的倾斜角为120°的几何性质将条件转化，在等边三角形PAF 中可得|PF|.【解析】选B.如图所示： ∵直线AF 的斜率为∴∠AFK=60°， ∴∠PAF=60°， 又|PA|=|PF|，∴△APF 为等边三角形， 在Rt △AKF 中，|FK|=4， ∴|AF|=8，∴|PF|=8.11.独具【解题提示】确定点P 到直线AB 的距离d ，利用S △ABP =12|AB|·d 求面积. 【解析】选C.设抛物线方程为y 2=2px ，则点C(p 2，0)，在方程中，令x=p 2，则y=〒6，即36=p 2，得p=6,∴y 2=12x ，∴点P 到直线AB 的距离为p=6， ∴S △ABP =12|AB|·6=36.12.【解析】选D.易知S 1=2ab ，S 2=2(a 2+b 2)， ∴()122222S 2ab ab ab 1S a b 2ab 22a b ==≤=++，当且仅当a=b 时取等号. 13.【解析】由222a b 1b b 3a a 2⎧+=⎪⎪⎨=⎪⎪⎩，得:2a 3b ⎧=⎪⎪⎨⎪=⎪⎩ ∴双曲线的渐近线方程为y=〒2x. 答案：y=14.【解析】，∴右焦点为(2，0)，e=c a=2，∴圆的方程为(x-2)2+y 2=4. 答案：(x-2)2+y 2=415.【解析】由题意b=c ，∴a 2=b 2+c 2=2c 2，∴e=c a2=.答案：216.独具【解题提示】△ABF 2的周长为4a ，求得a 的值，再由离心率求得c 的值，可得椭圆的方程.【解析】由△ABF 2的周长=4a=16,得a=4,即c a 进而c=所以a 2=16,b 2=a 2-c 2=16-8=8,∴C 的方程为22x y 1168+=.答案：22x y 1168+=17.【解析】∵椭圆22x y 1259+=的焦点坐标为(-4，0)和(4，0)，则可设双曲线方程为2222x y 1a b-=(a ＞0，b ＞0)，∵c=4，又双曲线的离心率等于2，即c a=2，∴a=2.∴b 2=c 2-a 2=12.故所求双曲线方程为22x y 1.412-=18.【解析】以拱顶为原点，水平线为x 轴，建立坐标系，如图，由题意知， |AB|=20，|OM|=4，A 、B 坐标分别为(-10，-4)、(10，-4)，设抛物线方程为x 2=-2py ，将A 点坐标代入， 得100＝-2p 〓(-4)，解得p=12.5，于是抛物线方程为x 2=-25y ， 由题意知E 点坐标为(2，-4)，E ′点横坐标也为2， 将2代入得y=-0.16，从而|EE ′|=(-0.16)-(-4)=3.84， 故最长支柱长应为3.84米.19.【解析】(1)依题意，圆M 的半径等于圆心M(-1，0)到直线的距离， 即，∴圆M 的方程为(x+1)2+y 2=4.(2)设P(x ，y)，由|PA|·|PB|=|PO|2，得22x y =+，即x 2-y 2=2.PA PB =(-2-x ，-y)·(2-x ，-y)=y 2+x 2-4=2x 2-6，由()2222x y 2x 1y 4⎧-=⎪⎨++=⎪⎩，解得:11x 22--+=舍)， ∵点P 在圆M内，∴x ≤， ∴2≤x2，∴-2≤2x2-6， ∴PA PB的取值范围是[-2).独具【误区警示】本题易出现的错误是利用点在圆内，求出-2＜y ＜2或-3＜x＜1，从而求出PA PB 的范围为［-2，6)或 [-6，12)，错误的原因是忽视了借助图像准确确定x 的范围，致使所求范围过大.20.【解析】(1)直线AB 的方程为y=-x+4，由2y x 4y 2px =-+⎧⎨=⎩，得：y 2+2py-8p=0，设A(x 1，y 1)，B(x 2，y 2)，∴y 1+y 2=-2p ，y 1y 2=-8p ，∴AB ==解得:p=2.(2)由(1)可知OA OB =x 1x 2+y 1y 2=2212y y 44 -8〓2=16-16=0， ∴OA ⊥OB.21.【解析】(1)依题意得：A(-2，0)，B(2，0),∴曲线E 的方程为y 2=8x. (2)由)2y x 1y 8x⎧=-⎪⎨=⎪⎩得：kx 2-(2k+8)x+k=0. 由()222k 84k 0,k 0⎧∆=+-⎪⎨⎪⎩＞＞∴k ＞0, 设M(x 1,y 1),N(x 2,y 2)， 则x 1+x 2=2k 8k+,x 1x 2=1. ∴AM AN =(x 1+2,y 1)·(x 2+2,y 2) =(x 1+2)(x 2+2)+y 1y 2=(k+1)x 1x 2+(2-k)(x 1+x 2)+4+k=161k+≥17,∴0＜k ≤1,∴θ∈(0,4π］.22.独具【解题提示】(1)利用a 、b 、c 的关系及离心率求出a ，b ，代入标准方程；(2)联立直线方程与椭圆方程，然后利用根与系数的关系，设而不求，整体代入.【解析】(1)由已知得c a = ,解得又b 2=a 2-c 2=4,所以椭圆G 的方程为22x y 1.124+=(2)设直线l 的方程为y=x+m ， 由22y x mx y 1124=+⎧⎪⎨+=⎪⎩得，4x 2+6mx+3m 2-12=0① 设A ，B 的坐标分别为(x 1,y 1),(x 2,y 2)(x 1＜x 2),AB 的中点为E(x 0,y 0),则x 0=12x x 2+=-3m4,y 0=x 0+m=m4.因为AB 是等腰△PAB 的底边，所以PE ⊥AB.所以PE 的斜率m24k 13m34-==--+,解得m=2.此时方程①为4x 2+12x=0,解得x 1=-3,x 2=0,所以y 1=-1,y 2=2.所以此时，点P(-3,2)到直线AB ：x-y+2=0的距离2=所以△PAB 的面积S=19AB d 22= .。
《学习方略》课时提升卷：单元质量评估(三)(鲁科版必修1)
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单元质量评估(三)第4、5章(90分钟100分)一、选择题(本大题共10小题,每小题4分,共40分。
每小题至少一个答案正确,选不全得2分)1.(2013·珠海高一检测)如图所示,质量为m的木块放在倾角为θ的斜面上静止不动,关于木块受到的支持力大小N和摩擦力大小f,下列选项正确的是( )A.N=mgcosθB.N=mgsinθC.f =mgsinθD.f=mgcosθ2.下列哪几组共点力作用在同一物体上,物体可能保持平衡( )A.2 N、5 N和9 NB.2 N、30 N和50 NC.8 N、18 N和9 ND.20 N、30 N和20 N3.(2012·上海高考)已知两个共点力的合力为50 N,分力F1的方向与合力F的方向成30°角,分力F2的大小为30 N。
则( )A.F1的大小是唯一的B.F2的方向是唯一的C.F2有两个可能的方向D.F2可取任意方向4.如图所示,在水平力F作用下,重为G的物体沿竖直墙匀速下滑,若物体与墙之间的动摩擦因数为μ,则物体所受摩擦力的大小为( )A.μFB.μF+GC.GD.5.(2013·邢台高一检测)如图所示,竖直放置的轻弹簧一端固定在地面上,另一端与斜面体P连接,P的斜面与固定挡板MN接触且处于静止状态,则斜面体P此刻所受的外力个数有可能为( )A.2个B.3个C.4个D.5个6.(2013·赤峰高一检测)如图所示,轻弹簧上端固定在天花板上,下端悬挂木块A,A处于静止状态,测得此时弹簧的伸长量为x(弹簧的形变在弹性限度内)。
已知木块A的质量为m,重力加速度为g,则此弹簧的劲度系数为( )A. B.C.mgxD.7.一块砖平放在长木板的中间,木板放在水平地面上,现缓慢抬起木板的一端,而保持另一端不动。
人教版必修一高中英语作业与测评单元质量评估(三).docx
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单元质量评估（三）Unit 3（120分钟150分）第I卷第一部分听力（共两节，满分30分）第一节（共5小题；每小题1. 5分，满分7. 5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1.Why is the man going to London?A.To live there・B・ To visit a friend.C. To work there.2.What is the woman looking for?A.Her camera.B. Her coat・C. Her plane ticket.3.When will the man go to the store?A.This Monday.B. Tomorrow.C. This weekend.4.Where does the conversation most probably take place?C. In the classroom.5.How much can one student save in the gallery?A・$2・ B. $8. C. $10.【听力材料】Text 1W: I heard you9re leaving.M: Yeah, I am moving to London. @Tve got a new job・W: Fll miss you.Text 2M: Oh, my God! Sophie, ifs already 9: 30. We have to get to the airport before 10 o，clock.W: But where is my camera? I can't find it anywhere. I need it to take pictures while we are in Shanghai.Text 3W: Do you have any special plans for 5 your weekend?M: Fm going to the store to buy a huge HDTV. I like watching sports programs. The screen of my present TV set is so small.Text 4W: Will you give me that book, please? ' The one in the second shelf! Here is my card. M: Here you are. You must be collecting information about the experiment, too.Text 5W: My dear, I hardly believe the admission price of the gallery is ~ ten dollars perperson. Ifs pretty expensive for a single exhibit.M: But if we have student cards, we can get in for two dollars・W: Really? Lefs have a try.答案:CACBB第二节（共15小题；每小题1. 5分，满分22. 5分）听下面5段对话。
Unit3单元质量评估(新人教版选修7)
Unit3单元质量评估（三）（新人教版选修7）Ⅱ. 单项填空(共15小题；每小题1分，满分15分)21. Teenagers should keep in mind that there’s something more important than ______ fashion for them to seek after in ______ life.A. /; theB. /; /C. the; /D. the; the22. Tom was so lucky tha t a fisherman who was fishing nearby ______ him ______ of the seawater after he fell off his boat.A. helped; outB. picked; outC. let; outD. blocked; out23. He urged ______ us the need for patience in doing this job.A. toB. onC. ofD. with24. Global food prices ______ very sharp increase during the year 2010 and they are continuing to rise further.A. observedB. witnessedC. provedD. supplied25. It is useless to attempt to______ from every danger: some risks must be taken.A. fleeB. hideC. hesitateD. run26. It’s not good manners for a lady to speak almost without ______ for breath; it’s very necessary to listen to others’ opinion.A. pausingB. standingC. predictingD. opposing27. It was several minutes before I was ______ of what happened.A. tiredB. accusedC. awareD. ashamed28. If I correct someone, I will do it with as much good humor and self-restraint as if I were the one ______.A. to be correctedB. correctingC. having being correctedD. being corrected29. The lost car of the Lees was found ______ in the woods off the highway.A. vanishedB. abandonedC. scatteredD. rejected30. The lack of eco-friendly habits among the public is thought to be a major ______ of global climate change.A. resultB. causeC. warningD. reflection31. The meeting is beginning at 8 o’clock. ______, let’s make some preparations for it.A. WhenB. MeanwhileC. WhileD. During32. As she was late again,Mary was scared ______ her boss because she was scared ______.A. to face; to be punishedB. to face; of being punishedC. of facing; of being punishedD. of facing; to be punished33. —I’m looking forward to your ______ here.—Sorry, I’m too busy and haven’t even a minute to ______.A. come; spareB. come; sparingC. coming; sparingD. coming; spare34. His laboratory has become the______, which was attacked by the animal rights groups for he had had drug trials on monkeys.A. exampleB. handleC. faceD. target35. All the leaders were ______ leave the hall when the explosion happened.A. able toB. about toC. sure toD. likely toⅢ. 完形填空（共20小题；每小题1. 5分，满分30分）A study, published in January in the US magazine, shows many people believe 36 are dangerous and will always try to hurt37 even kill humans. In fact, 94 percent of the world’s 400 species are harmless to humans. A shark 38 at the National Aquarium in Baltimore, US, proves this. Visitors can 39 young sharks, see their eggs deve lop and watch dozens of different species swim 40 around a huge tank. Most people41 to realize that shark attacks don’t happen very often. Humans are more42 to be killed by lightning than by a shark. And to make this point clear, the museum has43 a special touching pool for children. There, kids can learn, from an early age,44 sharks. They can watch them develop inside their eggs and feel the skin of the older swimmers. “People fear what they don’t know,” said Nancy Hotchkiss, an organizer of the exhibition, which runs45 December. “Sharks have been around for 400 million years and play an important role in the ocean’s food 46 . We want people to discover that sharks are47 animals that need our respect and 48 . ” A shocking 100 million sharks are killed every year around the world by humans. Scientists found that almost all recorded shark species have fallen 49 half in the past 8 to 15 years. Thousands of sharks are hunted in Asia for special foods,50 shark fin（鱼翅）soup. And many others get 51 in nets, while fishermen are hunting other fish.52 half of all sharks are smaller than one meter long. “Some fishing methods are actually 53 the ocean,” said Dave Schofield, the manager of the aquarium’s ocean health programme. “The fis hermen throw them away 54 rubbish. It is a worrying situation and some areas have put55 in place to protect these special fish. ”36. A. sharks B. fish C. animals D. beings37. A. and B. or C. but D. so38. A. talk B. filmC. TV playD. exhibition39. A. touch B. kill C. hurt D. buy40. A. hard B. frequentlyC. difficultyD. smoothly41. A. want B. begin C. fail D. attempt42. A. possible B. likelyC. probableD. lively43. A. stand up B. look upC. set upD. get up44. A. fear B. fearsC. not to fearD. to fear45. A. until B. when C. while D. as46. A. factory B. chain C. ship D. producer47. A. amazing B. happy C. shy D. cold48. A. punishment B. protectionC. preventionD. pollution49. A. by B. to C. in D. from50. A. for B. toC. for exampleD. such as51. A. to catch B. caught C. catching D. catch52. A. Rather than B. More thanC. LessD. Few53. A. cleaned B. cleaning outC. cleanD. cleaned54. A. as B. looking likeC. likeD. as if55. A. up B. rules C. value D. measuresⅣ. 阅读理解(共20小题；每小题2分，满分40分)(A)In October on the east coast of Australia migrating humpback whales (座头鲸) pass very close to the shore. With the help of Max Egan,we went to filmthem near Byron Bay. It was extremely exciting to spot the little puffs (水柱) of spray on the horizon. When migrating,the whales can be traveling at speeds of about 12 km/hour and can dive under anywhere between five and forty minutes, but with many years of experience Max usually guided our boat to exactly the right place to provide us with amazing sighting. As the whales break the surface like submarines (潜水艇),the water spills off their broad dark backs and huge tails. Then, with a powerful downstroke, they dive back into the depths of the sea, leaving just a smooth glassy patc h of water or “footprint” on the surface to indicate where they had been.On one day we had traveled up and down the shore and far out to sea in search of whales, but the horizon was deserted. There was no report of whales in the area so we decided to test out Max’s new, highly sensitive hydrophone (水下听音器) and the result was astonishing. As soon as the hydrophone was in the water, we found ourselves listening to the most beautiful voices. What may have seemed like a vast empty ocean was filled with the singing of whales.It is the males which sing, as they migrate between feeding and breeding grounds. No one knows for sure what the purpose of these songs is, whether they are love songs to the females or warnings to other males to stay away.It was thought that each population of humpbacks had its own song which remained constant but recent findings suggest that the whales appreciate a memorable tune and quickly adopt any new songs they hear.56. Which finding about whales is beyond the writer’s expectation?A. The little puffs.B. The songs of whales.C. The traveling speed of whales.D. The depth of the whale’s dive.57. What do we know about Max?A. He likes whales very much.B. He is a brave scientist on whales.C. He is an experienced man in finding whales.D. He is an expert in making hydrophones.58. The writer’s main purpose of looking for whales is ______.A. carrying out research on whalesB. studying the beautiful songs of whalesC. making films about whalesD. hunting whales for research59. What’s the WRONG opinion abou t whales before according to the passage?A. Each group of humpbacks had the song of their own.B. Whales can’t sing to each other.C. Whales aren’t easy to find.D. Whales can’t dive in the sea as long as forty minutes.(B)Dolphins（海豚）are not fish, but warm-blooded animals. Theylive in groups, and speak to each other in their own language. In thisway they are like other animals,such as bees and birds. Butdolphins are very different from almost all land animals. Their brainis nearly the same size as our own and they live a long time—at least twenty or thirty years.Like some animals, dolphins use sound to help them find their way around. They also make these sounds to talk to each other and to help them find food. We now know they do no t use their ears to receive these sounds,but the lower part of the mouth, called the jaw.Strangely, dolphins seem to like man, and for thousands of years there have been stories about the dolphin and its friendship with people.There is a story about sailors in the 19th century. In a dangerous part of the sea off the coast of New Zealand,they learnt to look for a dolphin called Jack. From 1871 to 1903,Jack met every boat in the area and showed it the way. Then in 1903 a passenger on a boat call ed The Penguin shot and wounded Jack. He recovered and for nine years more continued to guide all ships through the area—except for The Penguin.Today, some people continue to kill dolphins,but many countries of the world now protect them and in these places it is against the law to kill them.60. Dolphins are different from many other animals because they ______.A. live in groupsB. have large brainsC. are warm-bloodedD. have their own language61. Which of the following does the dolphin use to he lp it find its way around?A. Its nose.B. Its ears.C. Its mouth.D. Its eyes.62. Why did the sailors off the coast of New Zealand look for Jack?A. He was lonely and liked to be with people.B. They enjoyed playing with him.C. He was seriously wounded.D. They wanted his help.63. By telling the story of Jack the writer wanted to show that ______.A. dolphins are friendly and cleverB. people are cruel to animalsC. Jack is different from other dolphinsD. dolphins should be protected by law(C)Michael Fish may soon be replaced as a weather forecaster bysomething truly fishier—the shark (鲨鱼).Research by a British biology student suggests that sharkscould be used to predict storms.Lauren Smith,24,is close to completing her study on shark’sability to sense pressure.If her studies prove the theory,scientists may be able to monitor the behaviour of sharks to predict bad weather.Miss Smith had previously studied the behaviour of lemon sharks in theBahamas.She then used their close relatives,lesser spotted dogfish,for further research at Aberdeen University.Her work—thought to be the first of its kind to test the pressure theory—resulted from the observation that juvenile blacktip sharks off Flori da moved into deeper water ahead of a violent storm in 2001.Miss Smith said: “I’ve always been crazy about traveling and diving and this led me to an interest in sharks. ”“I was delighted to have been able to research in the area for my degree. I know there’s so much more we need to understand—but it certainly opens the way to more research. ”It has been discovered that a shark senses pressure using hair cells in its balance system.At the Bimini Shark Lab in the Bahamas, Miss Smith fixed hi-tech sensors to sharks to record pressure and temperature,while also tracking them using GPS (Global Positioning System) technology.In Aberdeen, she was able to study the effects of tidal(潮汐的) and temperature changes on dogfish—none of which were harmed. She also used a special lab which can mimic(模拟) oceanic pressure changes caused by weather fronts.She is due to complete her study and graduate later this year. She says she will be looking for a job which will give her the chance to enri ch her experience of shark research.64. The passage is most probably taken from ______.A. a short-story collectionB. a popular science magazineC. a research paperD. a personal diary65. What do we learn from the first four paragraphs of the passage?A. Sharks may be used to predict bad weather.B. Sharks’ behaviour can be controlled.C. Michael Fish is not qualified for his job.D. Lauren Smith will become a weather forecaster.66. Lauren Smith conducted her research by ______.A. removing hai r cells from a shark’s balance systemB. measuring the air pressure of weather frontsC. recording sharks’ body temperatureD. monitoring sharks’ reaction to weather changes67. What is the passage mainly about?A. A popular way of forecasting weather.B. A new research effort in predicting storms.C. Biologists’ interest in the secrets of sharks.D. Lauren Smith’s devotion to scientific research.(D)The Giant Squids（鱿鱼）in the Deep OceanJapanese scientists have taken the first photographs of oneof the most mysterious creatures in the deep ocean—the giantsquid.Until now the only information about the behavior of thecreatures which measure up to 18 meters(59 feet) in length hasbeen based on dead or dying squid washed up on shore or captured in commercial fishing nets.But Tsunemi Kubodera of the National Science Museum,and Kyoichi Mori of the Ogasawara Whale Watching Association, both in Tokyo have ca ptured the first images of Architeuthis attacking bait（鱼饵）900 meters below the surface in the cold, dark waters of the North Pacific. “We show the first wild images of a giant squid in its natural environment,”they said in a report in the journal Proceedings B of the Royal Society.Little is known about the creatures because it has been so difficult tolocate and study them alive. Large ships and specialist equipment,which is costly, are needed to study deep sea environments.The Japanese scientists found the squid by following sperm whales,the most effective hunters of giant squids,as they gathered to feed between September and December in the deep waters off the coast of the Ogasawara Islands in the North Pacific. They used a remote long-line camera and depth logging system to capture the giant squid in the ocean depths.The most dramatic character of giant squids is the pair of extremely long tentacles（触须）,distinct from the eight shorter arms. The long tentacles make up to two-thirds of the length of the dead specimens（标本，样本）to date. The giant squid appears to be a much more active meat-eating animal than researchers thought before.68. The passage mainly tells us that ______.A. scientists captured a giant squid aliveB. scientists captured a giant squid on cameraC. giant squids are spe cial meat-eating animalsD. giant squids mainly live in the deep sea69. According to the passage,we can infer that the underlined word “Architeuthis” should refer to ______.A. a scientistB. the sperm whaleC. a big shipD. the giant squid70. According to the passage, giant squids ______.A. like living in the cold and deep watersB. mainly feed on the dead fishC. like playing, using their tentaclesD. have only eight arms around the mouth71. According to the passage, the scientists located the giant squid _____.A. through a remote long-line cameraB. by using depth logging systemC. by following sperm whalesD. by using the bait to attract it(E)A child who has once been pleased with a tale likes, as a rule, tohave it retold in almost the same words, but this should not leadparents to treat printed fairy stories as formal texts. It is always muchbetter to tell a story than read it out from a book, and, if a parent canproduce what, in the actual circumstances(情况) of the time and theindividual child, is an improvement on the printed text,that’s muchbetter.A charge made against fairy tales is that they harm the children by frightening them or making them sad thinking. To prove the latter,one would have to show in a controlled ex periment that children who had read fairy stories were more often guilty of cruelty than those who had not. As to fears, there are, I think, some cases of children being strongly terrified by some fairy stories. This also arises from the child who has hear d the story once. However,familiarity with the story by repetition turns the pain of fear into the pleasure of a fear faced and mastered.There are also people who are opposed to fairy stories in that they are not true, that giants, witches, two-headed dragons, magic carpets, etc. do not exist; and that, instead of being fond of the strange side in fairy tales, the child should be taught how to adapt to reality by studying history and mechanics. I find such people, I must say so strange that I do not k now how to argue with them. If their cases were sound, the world should be full of mad men attempting to fly from New York to Philadelphia on a stick or covering a telephone with kisses in the belief that it was their beloved girlfriend.No fairy story has ever claimed(声称) to be description of the real world and no clever child has ever believed that it is.72.The author considered that a fairy story is more effective ______.A. when a story is repeated without any changeB. when we treat a story as a jokeC. when the parent makes some changes about a storyD. when the story is set in the present time73.According to the passage, a child can feel scared when a story is ____.A. in a realistic settingB. heard for the first timeC. repeated too oftenD. told in a different way74.What is the advantage claimed for repeating fairy stories to young children?A. Making them less fearful.B. Developing their power of memory.C. Making them believe there is nothing to be afraid of.D. Encouraging them not to have stran ge beliefs.75.According to the last paragraph, we can know ______.A. fairy stories are still being made upB. there are some misunderstandings about fairy talesC. people try to update old fairy storiesD. there is more concern for children’s fears now adays第Ⅱ卷（非选择题）Ⅴ. 书面表达（共1题；满分35分）假设你是李华，在出国交流学习期间，到当地一家电影院看了一场精彩的电影，但在观看电影过程中发现了一些问题。
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单元质量评估(三)第三章 三角恒等变形 (120分钟 150分)一、选择题(本大题共12小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的)1.已知cos(π+x)=35,x ∈(π,2π)，则sinx=( ) (A)35(B)45(C)35 (D)452.(2011·福建高考)若tan α=3,则2sin2cos 的值等于( )(A)2 (B)3 (C)4 (D)63.函数y=sin 2x+sinxcosx 的最小正周期T=( ) (A)π (B)2π (C)2 (D)34.已知tan θ=43，则sin cossin cos的值为( )(A)13 (B)13(C)7 (D)-75.已知α是第二象限角，且sin α=35，则tan2α=( )(A)247 (B)724 (C)724 (D)2476.设2132tan13acos6sin6,b 221tan 13, 1cos50c 2则有( ) (A)a>b>c (B)a<b<c (C)a<c<b (D)b<c<a 7.(2011·辽宁高考)设1sin()43，则sin2θ=( )(A)9 (B)9(C)9 (D)98.已知cos2θ=3，则sin 4θ+cos 4θ的值为( ) (A)1318 (B)1118 (C)79(D)-1 9.设cos(x+y)sinx-sin(x+y)cosx=1213，且y 是第四象限角，则ytan 2的值是( )(A)23 (B)32 (C)32 (D)2310.函数y=sin(3x+3)·cos(x-6)+cos(3x+3)·cos(x+3)的一条对称轴是( )(A)x=6(B)x=4(C)x=6(D)x=211.已知tan θ=2，则sin 2θ+sin θcos θ-2cos 2θ=( ) (A)45(B)54(C)34 (D)43 12.已知函数1cos2x x xf x asin cos()224sin(x)2(其中a≠0)的最大值为2，则常数a 的值为( )(C)二、填空题(本大题共4小题，每小题5分，共20分，请把正确的答案填在题中的横线上)13.函数y=2cos 2x+sin2x 的最小值是________. 14.已知3x x 3x xf x coscos sin sin 2sinxcosx 2222，当x ∈［2,π］时f(x)的零点为______.15.已知α是第二象限的角，tan(π+2α)=43，则tan α=______． 16.关于函数，下列命题： ①若存在x 1,x 2有x 1-x 2=π时，f(x 1)=f(x 2)成立；②f(x)在区间［,63］上单调递增；③函数f(x)的图象关于点(12,0)成中心对称图形；④将函数f(x)的图象向左平移512个单位后将与y=2sin2x的图象重合．其中正确的命题序号是__________ (注：把你认为正确的序号都填上).三、解答题(本大题共6小题，共70分，解答时应写出必要的文字说明、证明过程或演算步骤)17.(10分)(2011·保定高一检测)化简1sinx cosx sin2x1sinx cosx,并求出其最大值.18.(12分)已知1tan()42，试求式子2sin22cos1tan的值．19.(12分)已知函数f(x)=2sinxcosx-2cos2x+1，(1)求f(x)的最大值及相应的x的值；(2)若f(θ)=35，求cos2(4-2θ)的值．20.(12分)(2011·邯郸高一检测)已知向量a=(sinx,1),b=(cosx,12)(1)当a b时，求|a b|的值；(2)求函数f(x)=a·(2b-a)+cos2x的单调增区间.21.(12分)(2011·徐州高一检测)已知cosα=17,cos(α-β)=1314，且0<β<α<2.(1)求tan2α的值；(2)求β的值.22.(12分)(2011·北京高考)已知函数f(x)=4cosxsin(x+6)-1.(1)求f(x)的最小正周期；(2)求f(x)在区间［,64］上的最大值和最小值.答案解析1.【解析】选B.∵cos(π+x)= 35，∴-cosx=35，即cosx=35；又x ∈(π,2π)， ∴24sinx 1cos x5. 2.【解析】选D.22sin22sin cos2tan6cos cos . 3.【解析】选A. 21cos2x1y sin x sinxcosxsin2x 221121sin2x cos2xsin(2x )22242, ∴最小正周期T=π. 4.【解析】选C.41sin cos tan 1374sincostan113.5.【解析】选D.由α是第二象限角且sin α=35得cos α=45； ∴sin2α=2sin αcos α=2425， cos2α=cos 2α-sin 2α=725；∴sin224tan2cos27．6.【解析】选C.a=sin30°cos6°-cos30°sin6°=sin24°,b=sin26°, c=sin25°,根据正弦函数的单调性知选C.7.【解析】选A.sin2θ=-cos(2+2θ)=-cos2(4+θ)=2sin 2(4+θ)-1=79. 8.【解析】选B.sin 4θ+cos 4θ=(sin 2θ+cos 2θ)2-2sin 2θcos 2θ=1-12sin 22θ=1-2(1-cos 22θ) =18. 9.【解析】选D.由cos(x+y)sinx-sin(x+y)cosx=1213得sin ［x-(x+y)］=-siny=1213， 又∵y 是第四象限角， ∴cosy=513，∵y 1cosytan2siny5121312313. 10.【解析】选D.y=sin(3x+3)·cos(x-6)+cos(3x+3)·cos(x+3)=sin(3x+3)cos(x-6)-cos(3x+3)sin(x-6)=sin(2x+2)=cos2x, 其对称轴为x=k2(k ∈Z)，当k=1时x=2. 11.【解析】选A.sin 2θ+sin θcos θ-2cos 2θ2222sin sin cos 2cos sin cos22tan tan 24224tan 1415. 12.【解析】选C. 22cos x x x 1af xasin coscosx sinx 4cosx222221a sin(x)44,(其中tan =1a);244,∴a=13.【解析】sin(2x+4)+1，所以最小值为.答案：14.【解析】cos(2x+4),令f(x)=0cos(4+2x)=0，又∵x ∈［2,π］，∴592x444， ∴32x42， ∴x=58，即函数f(x)的零点是58. 答案: 5815.【解析】由tan(π+2α)= 43得tan2α=43， 又22tan 4tan21tan 3，解得tan α=12或tan α=2，又a 是第二象限的角，所以tan α=12.答案：1216.独具【解题提示】先利用三角恒等变换将函数f(x)化为f(x)=Asin(ωx+ )+k的形式，再判断其命题的真假.【解析】∵sin2x=2sin(6-2x)=2sin(2x+56)=2sin2(x+512)， ∴周期T=π，①正确；∵递减区间是532k2x2k 262(k ∈Z)，解之为kxk63(k ∈Z)，②错误；∵对称中心的横坐标为5k 52xkx6212，当k=1时，得③正确；应该是向右平移，④不正确． 答案：①③ 17.【解析】原式=1sin2x sinx cosx1sinx cosx2sinx cosx sinx cosx1sinx cosx=sinx-cosx2sin(x)4，.18.【解析】22sin22cos 2cos (tan1)1tan1tan=2cos 2α·tan(α- 4)22cos ()1cos22422sin ()241(1cos2)22cos2tan()44tan()422sin(2)221tan ()414()222.151()2［］［］19.【解析】(1)f(x)=sin2x-(2cos 2sin(2x-4).∴当2x-4=2k π+2，即x=k π+38π(k ∈Z)时，f(x)(2)由f(θ)=sin2θ-cos2θ，及f(θ)= 35得： sin2θ-cos2θ=35，两边平方得1-sin4θ=925，即sin4θ=1625； ∴cos2(4-2θ)=cos(2-4θ)=sin4θ=1625.20.独具【解题提示】先根据向量的相关知识转化成三角关系式，然后再利用三角恒等变换研究相关问题. 【解析】(1)当a b 时，a ·b =0，∴|ab |=22a2a bb2213sin x 1cos x42. (2)f(x)=2a ·b-a 2+cos 2x=2sinxcosx-1-sin 2x-1+cos 2x sin(2x+4)-2,当2k π- 2≤2x+4≤2k π+ 2 (k ∈Z)时f(x)单调递增,解得k π-38≤x ≤k π+8(k ∈Z),∴函数f(x)的单调增区间为［k π-38,k π+8］,(k ∈Z) 21.【解析】(1)cos α=17,0<α<2， 得22143sin 1cos 1()7, ∴sin43tan743cos7,于是222tan 24383tan21tan 1(43). (2)由0<β<α<2，得0<α-β<2,又∵cos(α-β)= 1314，∴221333sin()1cos ()1()14, ∴cos β=cos ［α-(α-β)］ =cos αcos(α-β)+sin αsin(α-β)113433317147142, 又0<β<2,∴β= 3.22.【解析】(1)因为f(x)=4cosxsin(x+6)-1=4cosx(2sinx+12cosx)-1sin2x+2cos2x-1sin2x+cos2x=2sin(2x+6).所以f(x)的最小正周期为π.(2)因为x64,所以22x663,于是,当2x62,即x=6时，f(x)取得最大值为2;当2x66,即x=-6时，f(x)取得最小值为-1.独具【方法技巧】三角函数最值的求法：(1)利用单调性,结合函数图象求值域,如转化为y=asin(ωx+)+b型的值域问题.(2)将所给的三角函数转化为二次函数,通过配方法求值域,如转化为y=asin2x+bsinx+c型的值域问题.(3)换元法,出现sinx+cosx,sinx-cosx,sinxcosx时常令t=sinx+cosx,转化为二次函数值域的问题.换元前后要注意等价. 面对强大的对手，明知不敌，也要毅然亮剑，即使倒下，也要化成一座山。